HF=HM IV: The Seiberg-Witten Floer homology and ech correspondence

Abstract

This is the fourth of five papers that construct an isomorphism between the Seiberg-Witten Floer homology and the Heegaard Floer homology of a given compact, oriented 3-manifold. The isomorphism is given as a composition of three isomorphisms; the first of these relates a version of embedded contact homology on an an auxillary manifold to the Heegaard Floer homology on the original. The second isomorphism relates the relevant version of the embedded contact homology on the auxilliary manifold with a version of the Seiberg-Witten Floer homology on this same manifold. The third isomorphism relates the Seiberg-Witten Floer homology on the auxilliary manifold with the appropriate version of Seiberg-Witten Floer homology on the original manifold. The paper describes the second of these isomorphisms.

References in corpus (3)

• HF=HM I : Heegaard Floer homology and Seiberg--Witten Floer homology
• HF=HM III: Holomorphic curves and the differential for the ech/Heegaard Floer correspondence
• HF=HM II: Reeb orbits and holomorphic curves for the ech/Heegaard-Floer correspondence

Cited by in corpus (26)

• HF=HM I : Heegaard Floer homology and Seiberg--Witten Floer homology
• The equivalence of Heegaard Floer homology and embedded contact homology III: from hat to plus
• A combinatorial spanning tree model for knot Floer homology
• Embedded contact homology and open book decompositions
• Connected sums and involutive knot Floer homology
• A contact invariant in sutured monopole homology
• A splitting theorem for the Seiberg-Witten invariant of a homology $S^1\times S^3$
• On the Frøyshov invariant and monopole Lefschetz number
• Instanton Floer homology, sutures, and Heegaard diagrams
• On the monopole Lefschetz number of finite order diffeomorphisms
• Bordered Floer homology and incompressible surfaces
• Duality and mapping tori in Heegaard Floer homology
• On the equivalence of contact invariants in sutured Floer homology theories
• Equivariant Seiberg-Witten-Floer cohomology
• A survey of the homology cobordism group
• Noncommutative Hodge-to-de Rham spectral sequence and the Heegaard Floer homology of double covers
• Instanton Floer homology, sutures, and Euler characteristics
• Cobordism maps in embedded contact homology
• Dimensionally-reduced sutured Floer homology as a string homology
• Brieskorn spheres, cyclic group actions and the Milnor conjecture
• Formal Contact Categories
• Seiberg-Witten Floer Spectra and Contact Structures
• Seiberg-Witten Floer homotopy contact invariant
• Foliations, contact structures and their interactions in dimension three
• Knot Floer homology and the fundamental group of $(1,1)$ knots
• Taut foliations from knot diagrams